Does anyone know if persistent homology with integer coefficients are being used anywhere?
From what I understand, Carlsson's persistent module theory (http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.116.2471&rep=rep1&type=pdf) works well for field coefficients (only).
Quote: "The correspondence established by Theorem 3.1 suggests the non-existence of simple classifications of persistence modules over a ground ring that is not a field." (pg 7 of the paper)
Thanks for any help.